Always-On Quantum Error Tracking with Continuous Parity Measurements

Razieh Mohseninia; Jing Yang; Irfan Siddiqi; Andrew N. Jordan; Justin Dressel

doi:10.22331/q-2020-11-04-358

Always-On Quantum Error Tracking with Continuous Parity Measurements

Razieh Mohseninia^1,2, Jing Yang³, Irfan Siddiqi^4,5, Andrew N. Jordan^3,1, and Justin Dressel^1,6

¹Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
²Departments of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
³Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
⁴Center for Quantum Coherent Science, Berkeley, CA 94720 USA
⁵Department of Physics, University of California, Berkeley, CA 94720 USA
⁶Schmid College of Science and Technology, Chapman University, Orange, CA 92866, USA

Published:	2020-11-04, volume 4, page 358
Eprint:	arXiv:1907.08882v2
Doi:	https://doi.org/10.22331/q-2020-11-04-358
Citation:	Quantum 4, 358 (2020).

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Abstract

We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates passive error tracking in real time. It reduces overhead from the standard gate-based approach that periodically entangles and measures additional ancilla qubits. However, the noisy analog signals from continuous parity measurements mandate more complicated signal processing to interpret syndromes accurately. We analyze the performance of several practical filtering methods for continuous error correction and demonstrate that they are viable alternatives to the standard ancilla-based approach. As an optimal filter, we discuss an unnormalized (linear) Bayesian filter, with improved computational efficiency compared to the related Wonham filter introduced by Mabuchi [New J. Phys. 11, 105044 (2009)]. We compare this optimal continuous filter to two practical variations of the simplest periodic boxcar-averaging-and-thresholding filter, targeting real-time hardware implementations with low-latency circuitry. As variations, we introduce a non-Markovian ``half-boxcar'' filter and a Markovian filter with a second adjustable threshold; these filters eliminate the dominant source of error in the boxcar filter, and compare favorably to the optimal filter. For each filter, we derive analytic results for the decay in average fidelity and verify them with numerical simulations.

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► BibTeX data

@article{Mohseninia2020alwaysquantumerror,
  doi = {10.22331/q-2020-11-04-358},
  url = {https://doi.org/10.22331/q-2020-11-04-358},
  title = {Always-{O}n {Q}uantum {E}rror {T}racking with {C}ontinuous {P}arity {M}easurements},
  author = {Mohseninia, Razieh and Yang, Jing and Siddiqi, Irfan and Jordan, Andrew N. and Dressel, Justin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {358},
  month = nov,
  year = {2020}
}

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